Identities: Cofunction, Double-Angle and Half-Angle Section 7.2 Identities: Cofunction, Double-Angle and Half-Angle Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

Objectives Use cofunction identities to derive other identities. Use the double-angle identities to find function values of twice an angle when one function value is known for that angle. Use the half-angle identities to find function values of half an angle when one function value is known for that angle. Simplify trigonometric expressions using the double-angle identities and the half-angle identities.

Cofunction Identities

Example Prove the identity Solution:

Cofunction Identities

Example Find an identity for each of the following. Solution:

Double-Angle Identities

Other Useful Identities

Example Find an equivalent expression for each of the following. Solution:

Example (cont)

Half-Angle Identities

Example Find tan (π/8) exactly. Then check the answer using a graphing calculator in RADIAN mode. Solution:

Example Simplify each of the following. Solution: